World number one and defending champion Serena, trying to break the record of 22 grand slam titles she shares with Steffi Graf, plays number 52 Yaroslava Shvedova of Kazakhstan.
Sixth seed Venus, twice the champion in New York, faces Karolina Pliskova, the big-serving 10th seed from the Czech Republic. Victory for both would put them one win away from a semi-final meeting at Flushing Meadows.
Top seed Serena is still managing the right shoulder injury she suffered at the Rio Olympic Games last month but says she is ready to hit peak form.
“I feel OK,” she said when asked to grade her performance in week one. “So far, so good.
“I don't feel like I'm Serena out there yet, but hopefully she'll come around the second week.”
Venus is into the fourth round for the second straight season, having gone four years without passing round three while she learned to cope with Sjogren’s syndrome, an auto-immune disease that causes chronic fatigue and muscle soreness.
“It's just a lot of will power,” Venus said. “That's really what it is. I started to feel better more consistently this year so I'm always trying to find things to help me feel my best.
“But even if I'm not feeling great, I still manage to get a good fight in out there.”
Men’s second seed Andy Murray, the Wimbledon and Olympic champion, takes on Grigor Dimitrov for a place in the quarter-finals.
Former champion Juan Martin del Potro, in the fourth round for the first time since 2012 after three operations on his left wrist, plays eighth seed Dominic Thiem.
Third seed Stan Wawrinka, sixth seed Kei Nishikori and women’s fourth seed Agnieszka Radwanska are also in fourth-round action.
(Editing by Rex Gowar)
